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2 answers:
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Answer:
The vertical angles are ∠ WRS and ∠ VRT ⇒ 2nd answer
Step-by-step explanation:
* <em>Lets explain the meaning of the vertical angles</em>
- Vertical angles are the angles opposite to each other when two lines
are intersected
- The vertical angle are equal in measures
- <em>Look to attached figure which represents the lines </em>
∵ Line TW intersects line SV at R
∴ ∠ WRV and ∠ SRT are vertical angle
∴ <u><em>∠ WRS and ∠ VRT</em></u> are vertical angle
∵ RU is between the rays of angle VRW
∴ RU intersects the lines TW and SV at R
∴ No vertical angles between RU and the other two lines because
it intersects them its endpoint R
* <em>Now lets look to the answer to chose the right one</em>
- ∠ WRU and ∠ SRT are not vertical angles
- <em><u>∠ WRS and ∠ VRT are vertical angles </u></em>
- ∠ VRU and ∠ TRS are not vertical angles
- ∠ VRT and ∠ SRT are not vertical angles
Answer:
Step-by-step explanation:
The explanation of given question is described below:
Here, the test of hypothesis states that
The test statistic is
= 2.1
According to the given data α = 0.05,
So, the major value is
(refer to the standard normal table) .
Finally
Answer:
8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears
Step-by-step explanation:
For each account, there are only two possible outcomes. Either they are at least 1 month in arrears, or they are not. The probability of an account being at least 1 month in arrears is independent from other accounts. So the binomial probability distribution is used to solve this question.
However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that fewer than 82 accounts in the sample were at least 1 month in arrears
This probability is the pvalue of Z when X = 82. So
has a pvalue of 0.0885.
8.85% probability that fewer than 82 accounts in the sample were at least 1 month in arrears